A new class of state space models for longitudinal discrete response data, where the observation equation is specified in an additive form involving both deterministic and dynamic components is proposed. These models allow us to explicitly address the effects of trend, seasonal or other time-varying covariates, while preserving the power of state space models in modeling dynamic pattern of data. Different Markov chain Monte Carlo algorithms to carry out statistical inference for models with binary and binomial responses are developed. In a simulation experiment the mixing and convergence properties of these algorithms are investigated. In particular, it can be demonstrated that a joint state variable update is preferable over individual updates. In addition, different prior choices are studied. Finally, the applicability of the proposed state space mixed models for constructing individual risk profiles of migraine headache paients is illustrated.